MATLAB Array: Create and Define Types

Introduction to Arrays

Mathematical arrays are all around us. If
you take the time to process nature, even your own self, you’ll realize that
there is an ordered array of objects in the Universe. The solar system itself
has the planets orbiting around the sun in an ordered pattern. Cells are
organized in a geometric array, and additionally, in images like the above
organisms can create physical structures that have a geometric order to them.
Order is the nature of the Universe. In a similar manner, the aim of science
and mathematics is to model this order using numbers.

Mathematical arrays, similar to the image
above, is a reference to a set of numbers or objects in a specific pattern.
This is an organized pattern of numbers in a matrix containing rows and
columns. Mathematical manipulations of arrays can then be conducted, once the
the data is arranged in a suitable array.

Matrices are used for a variety of
applications in both science and engineering. The purpose of this tutorial is
to identify the different ways that matrices can be represented in the MATLAB
R2018b environment.

MATLAB, as a matrix based system is
composed of a series of multi-dimensional arrays of data. Due to the various
syntaxes that the system possesses, we will attempt to discuss the surface
discussions, and then delve into the details of any interesting topics in later
tutorials.

The rules for matrix arithmetic are
straight forward, and MATLAB is equipped to handle the manipulations of
hundreds of thousands of variables. While different from general mathematics,
matrix arithmetic has its merits when it comes to detailed science and
engineering calculations. With matrix arithmetic – addition, multiplication,
multiplication by a scalar, finding the inverse, are a few simple manipulations
that the system can facilitate.

MATLAB Array Brief Tutorial

For the purposes of this tutorial, let us
go through the process of describing some Matrix functions, and manipulating
them in the MATLAB user environment.

Starting with a fresh command page, we will
start the process of entering some arrays into the MATLAB system. The simplest
matrix that exists in the system is the zero matrix. This matrix is comprised
of all zeroes in the rows and all zeroes in the columns. The MATLAB syntax
enables you to determine the number of rows that you want to have in your
matrix.

Let’s start with the following code:

zeros(7)

Entering the code into MATLAB, the
system will process, and generate the following output:

Additionally,
if you so desire to create matrices of varying columns of the number one, you
can use the following code:

ones(5,8)

As you can see from the above syntax, the column identity is
in the first numeral of the syntax (5 in this instance), while the rows are
denoted by the second numeral after the comma. This is the numeral 8 in this
instance. Generating the one matrix can allow the user to facilitate further
downstream manipulations.

If
you want to get really creative with your matrices, you can use the rand()
function in MATLAB. This function is one that allows the system, in a lottery
like fashion, to create matrix arrays. Depending on the types of simulations
that you may be running, this function will come in handing for testing and
validating your data, after you have generated a mathematical model. Let us see
what happens when the following code is entered in the system.

rand(6, 9)

In a previous matrix transformation
tutorial we had encountered the magic square. While for the most part, you’ll
use this when you’re in the process of learning your MATLAB syntax, for grins,
let’s go ahead and go through the process of finding out what happens when we
use the magic function on a matrix that contains five rows. Now’s the time to
use our imaginations, so let’s go ahead and let MATLAB work it’s magic. Waving
our wands, and letting MATLAB calculate, the following is what we see:

magic(5)

Voila! What do we find when we enter the magic rubric into
our command center? This is the matrix…where the same sum is generated on all
aspects of the matrix. Whether you add all the components of a row, a column or
a diagonal, you end up with the same sum. Again, this is one of those matrices
that you play with initially, but eventually when you are validating a model,
later down the line, and need input of a certain format, it will be helpful to
you to know this function.

When it comes to arrays, there are a
myriad of options available in the MATLAB pool, that facilitate the desired
function. The following detailed table, outlines the functions that are
available to the user when it comes to the world of arrays. Ordering numbers is
just the first step, the second is the use of that data to generate
information.

Conclusion

As you venture into the world of MATLAB, you’ll realize that there are a myriad of ways that you can utilize matrix arrays to organize and manipulate your data. Taking the time to understand the syntax will be key to ensuring that your scientific or engineering systems are operating at their best. The key to good process modeling, is ensuring that you’re adequately represent your system well. The matrix is that ideal data organization format, and it allows infinite possibilities where data transformation from a mathematical perspective is concerned. Allow yourself to become familiar with the system, in order to achieve the utmost in your operational needs.

References

Tandose Sambo is a Chemical Process Engineer, with a focus on improving process efficiency via operational improvements. Six-Sigma certified, and with a Design-focus and Data Analytics interest, she is a driven growing entrepreneur, with the intention to optimize industrial and business process operations. Her interests include sharing time with family and travelling.

Tandose Sambo is a Chemical Process Engineer, with a focus on improving process efficiency via operational improvements. Six-Sigma certified, and with a Design-focus and Data Analytics interest, she is a driven growing entrepreneur, with the intention to optimize industrial and business process operations. Her interests include sharing time with family and travelling.